Answer :
Answer:
[tex]a_9_6=-1,234[/tex]
Step-by-step explanation:
we know that
The rule to calculate the a_n term in an arithmetic sequence is
[tex]a_n=a_1+d(n-1)[/tex]
where
d is the common difference
a_1 is the first term
n is the number of terms
we have
[tex]1,-12,-25,...[/tex]
Remember that In an Arithmetic Sequence the difference between one term and the next is a constant. and this constant is called the common difference
so
[tex]a_1=1\\a_2=-12\\a_3=-25[/tex]
[tex]d=a_2-a_1=-12-1=-13[/tex]
Find the 96th term of the arithmetic sequence
[tex]a_n=a_1+d(n-1)[/tex]
we have
[tex]a_1=1\\d=-13\\n=96[/tex]
substitute
[tex]a_9_6=1+(-13)(96-1)[/tex]
[tex]a_9_6=1+(-13)(95)[/tex]
[tex]a_9_6=1-1,235[/tex]
[tex]a_9_6=-1,234[/tex]